In an automatic coffee machine according to publication EP 0 761 150, corresponding to U.S. Pat. No. 5,957,033, a coffee grinder integrated into the coffee machine makes it possible to prepare coffee with coffee powder that is always freshly ground. This coffee grinder is equipped with two grinding discs that can be rotated in opposite directions in the conventional manner. In order to vary the degree of grinding which defines the grain size of the ground material as required, there is provided in the carrier of the one grinding disc a thread that can be screwed in and out within the body of the grinder, the effect of which is that the distance between the grinding discs can be adjusted by rotating the carrier manually. It is not possible to set the degree of grinding accurately and to keep it constant with these coffee grinders. Moreover, the manual handling is disadvantageous.